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Signalling Games
and Pragmatics
Anton Benz
University of Southern Denmark,
IFKI, Kolding
The course
concentrates on Gricean Pragmatics,
 is concerned with the foundation of
pragmatics on Lewis (1969) theory of
Conventions,
 uses classical game theory!

The course
 is
introductory!
The course is
not an introduction to the economic
literature on signalling games (cheap talk,
market signals, pragmatics of debate,
credibility).
 not concerned with the evolution of
language structure and its use
 no evolutionary game theory!

Other misleading expectations
Signalling Games and Pragmatics is not
related to:
 Wittgenstein’s Language Games.
 Game Theoretic Semantics (Hintikka).
Overview
Day 1: Introduction: From Grice to Lewis
 Day 2: Basics of Game and Decision
Theory
 Day 3: Two Theories of Implicatures
(Parikh, Jäger)
 Day 4: Best Answer Approach
 Day 5: Utility and Relevance

From Grice to Lewis
Day 1 – August, 7th
Overview

Gricean Pragmatics
 General
assumptions about conversation
 Conversational implicatures


Game and Decision Theory
Lewis on Conventions
 Examples
of Conventions
 Signalling conventions
 Meaning in Signalling systems
Gricean Pragmatics
General assumptions about
conversation
A simple picture of communication
The speaker encodes some proposition p
 He sends it to an addressee
 The addressee decodes it again and
writes p in his knowledgebase.


Problem: We communicate often much
more than we literally say!
Some students failed the exam.
+> Most of the students passed the exam.
Gricean Pragmatics
Grice distinguishes between:
 What is said.
 What is implicated.
“Some of the boys came to the party.”
said: At least two of the boys came to the party.
 implicated: Not all of the boys came to the party.

Both part of what is communicated.
Assumptions about Conversation

Conversation is a cooperative effort.

Each participant recognises in the talk
exchange a common purpose.

A stands in front of his obviously
immobilised car.
A: I am out of petrol.
B: There is a garage around the corner.

Joint purpose of B’s response: Solve A’s
problem of finding petrol for his car.
The Cooperative Principle
Conversation is governed by a set of
principles which spell out how rational
agents behave in order to make language
use efficient.
The most important is the so-called cooperative principle:
“Make your conversational contribution such
as is required, at the stage at which it
occurs, by the accepted purpose or
direction of the talk exchange in which you
are engaged.”
The Conversational Maxims
Maxim of Quality:
1. Do not say what you believe to be false.
2. Do not say that for which you lack adequate
evidence.
Maxim of Quantity:
1. Make your contribution to the conversation as
informative as is required for he current talk
exchange.
2. Do not make your contribution to the conversation
more informative than necessary.
Maxim of Relevance:
Make your contributions relevant.
Maxim of Manner:
Be perspicuous, and specifically:
1. Avoid obscurity.
2. Avoid ambiguity.
3. Be brief (avoid unnecessary wordiness).
4. Be orderly.
The Conversational Maxims
(short, without Manner)
Maxim of Quality: Be truthful.
Maxim of Quantity:
1. Say as much as you can.
2. Say no more than you must.
Maxim of Relevance: Be relevant.
The Conversational Maxims
Be truthful (Quality) and say as
much as you can (Quantity)
as long as it is relevant
(Relevance).
Conversational implicatures
An example: Scalar Implicatures
“Some of the boys came to the
party.”
 said:
At least two of the boys came to
the party.
 implicated: Not all of the boys came
to the party.
Both part of what is communicated.
An Explanation based on Maxims
Let A(x)  “x of the boys came to the party”
1. The speaker had the choice between the forms
A(all) and A(some).
2. A(all) is more informative than A(some) and
the additional information is also relevant.
3. Hence, if all of the boys came, then A(all) is
preferred over A(some) (Quantity) +
(Relevance).
4.
5.
6.
The speaker said A(some).
Hence it cannot be the case that all
came.
Therefore some but not all came to the
party.
A Graphical Interpretation I
The speaker has a choice between A(all)
and A(some).
 If he chooses A(all), the hearer has to
interpret ‘all’ by the universal quantifier.
 If he chooses A(some), the hearer has to
interpret ‘some’ by the existential
quantifier.

The situation were all of the boys
came to the party:
Taking into account the alternative situation
where some but not all came:
Adding speaker’s preferences:
Adding speaker’s preferences:
(Quantity): Say as
much as you can!
Hence, the speaker will choose:
Hence, the hearer can infer after
receiving A(some) that:
He is in this
situation
Game and Decision
Theory
Game Theory
“A game is being played by a group of
individuals whenever the fate of an
individual in the group depends not only
on his own actions but also on the actions
of the rest of the group.” (Binmore, 1990)
Game Theory and Pragmatics
In a very general sense we can say that we play a
game together with other people whenever we
have to decide between several actions such
that the decision depends on:
 the choice of actions by others
 our preferences over the ultimate
results.
Whether or not an utterance is successful depends
on
 how it is taken up by its addressee
 the overall purpose of the current conversation.
Decision Theory
If a decision depends only on
 the state of the world,
 the actions to choose from and
 their outcomes
but not on
 the choice of actions by other agents,
then the problem belongs to decision theory.
Remark
The situation depicted in the graph for scalar
implicatures is a problem for decision theory!


Decision theory: decisions of individual agents
Game theory: interdependent decisions of
several agents.
Why a New Framework?
Basic concepts of Gricean pragmatics are
undefined, most notably the concept of
relevance.
 On a purely intuitive level, it is often not
possible to decide whether an inference of
an implicatures is correct or not.

An Example
A stands in front of his obviously
immobilised car.
A: I am out of petrol.
B: There is a garage around the
corner. (G)
+> The garage is open (H)
A “standard” explanation
Set H*:= The negation of H




B said that G but not that H*.
H* is relevant and G  H*  G.
Hence if G  H*, then B should have said
G  H* (Quantity).
Hence H* cannot be true, and therefore
H.
A Second Explanation
B said that G but not that H.
2. H is relevant and G  H  G.
3. Hence if G  H, then B should have said
G  H (Quantity).
4. Hence H cannot be true, and therefore
H*.
Problem: We can exchange H and H* and
still get a valid inference.
1.
Without clarification of its basic
concepts, the theory of conversational
implicatures lacks true predictive
power.
Lewis on Conventions
(1969)
Lewis on Conventions
Lewis Goal: Explain the conventionality of
language meaning.
 Method: Meaning is defined as a property
of certain solutions to signalling games.
 Achievement: Ultimately a reduction of
meaning to a regularity in behaviour.

Lewis on Conventions
1.
2.
3.
4.
Some Examples of Conventions
Lewis’ Definition of Convention
Signalling Games and Conventions
Meaning in Signalling Games
Examples of Conventions
Examples of Conventions I
Driving Left or Right
All drivers have an interest to avoid
crashes.
 If two drivers meet driving in opposite
directions, then they have to agree who
drives on which side of the street.
 In each region or country developed a
convention which tells the drivers which
side to choose.

Driving Left or Right
Left
Right
Left
1, 1
0, 0
Right
0, 0
1, 1
Examples of Conventions II
Hume’s boat rowers
Suppose that there are two rowers in a boat.
 Both have an interest to let the boat float
smoothly and in straight direction.
 This they can only achieve if they row with the
same rate.
 Hence, the rowers will constantly adjust their
rates such that they meet the rate of their
partner.
Hume’s boat rowers
Examples of Conventions III
Rousseau’s stag hunters
There is a party of hunters.
 They have the possibility to hunt stag together or hunt
rabbit individually.



If they hunt stag together, they are provided with meat for several
days.
If they hunt individually, then they can only hunt rabbit which
provides them with meet for only one day.
They have only success hunting stag if everybody joins
in.  If one hunter drops out, then all others who still go
for stag will achieve nothing.
Rousseau’s stag hunters
Stag
Rabbit
Stag
2, 2
0, 1
Rabbit
1, 0
1, 1
Examples of Conventions IV
Lewis’ fire collectors
There is a party of campers looking for fire
wood.
 It does not matter to anyone which area he
searches but
 everyone has an interest not to search the
same place which has already been
searched by another member of the party.
Lewis’ fire collectors
North
South
North
0, 0
1, 1
South
1, 1
0, 0
Lewis’ Definition of Convention
(Lewis, 2002, p. 58)
A regularity R in the behaviour of members of a
population P when they are agents in an
recurrent situation S is a convention if and only if
it is true that, and is common knowledge in P
that, in any instance of S among member of P,
1.
2.
3.
everyone conforms to R;
everyone expects everyone else to conform to R;
everyone prefers to conform to R under the condition
that the others do, since S is a coordination problem
and uniform conformity to R is a coordination
equilibrium in S.
Analysis of Conventions
Conventions are solutions to a
coordination problem.
 The coordination problem is a recurrent
coordination problem.
 A convention consists in a regularity in
behaviour.

Everyone expects the others to follow the
convention.
 A true convention has to be an arbitrary
solution to the coordination problem.


In order to count as a true convention, it must be
in everybody’s interest that everybody follows
the convention.
Representations of Regularities of
Behaviour
A regularity in behaviour can be represented
by an agent’s strategy:
 A function that tells for each type of
situation which action the agent will
perform.
S : Situation-type  Actions
Signalling Conventions
(preliminary – simple cases)
The Coordination Problem in
Communication
The speaker wants to communicate some
meaning M.
 In order to communicate this he chooses a
form F.
 The hearer interprets the form F by
choosing a meaning M’.
 Communication is successful if M=M’.

The Signalling Game




Let F be a set of forms and M a set of
meanings.
The speaker’s signalling strategy is a function
S:MF
The hearer’s interpretation strategy is a function
H:FM
Speaker and hearer have success if always
S(M) = F  H(F) = M
Lewis’ Signalling Convention

A solution to the signalling game is a
strategy pair (S,H).

A strategy pair (S,H) with
S : M  F and H : F  M
is a signalling convention if
HS = id|M
Meaning in Signalling Games
Meaning in Signalling Conventions
Lewis (IV.4,1996) distinguishes between
 indicative signals
 imperative signals
Two different definitions of meaning:


Indicative:
A form F signals that M if S(M)=F
Imperative:
A form F signals to interpret it as H(F)
Two possibilities to define meaning.
 Coincide for signalling conventions in
simple signalling games.
 Lewis defines truth conditions of signals F
as S1(F).

The Paul Revere Examples
A scene from the American War of
independence:
The sexton of the Old North Church informs
Paul Revere about the movements of the
British troops, the redcoats. The only
possibility to communicate with each other
is by use of lanterns. A possible signalling
strategy of the sexton may look as follows:
A Possible Signalling Strategy
1.
2.
3.
If the redcoats are observed staying
home, hang no lantern in the belfry;
If the redcoats are observed setting out
by land, hang one lantern in the belfry;
If the redcoats are observed setting out
by sea, hang two lanterns in the belfry.
An Interpretation Strategy
1.
2.
3.
If no lantern is observed hanging in the
belfry, go home;
If one lantern is observed hanging in the
belfry, warn the countryside that the
redcoats are coming by land;
If two lanterns are observed hanging in
the belfry, warn the countryside that the
redcoats are coming by sea.
Representation of strategies
S
H
stay
land
sea
states
0
1
2
lanterns
0
1
2
lanterns
stay
land
sea
states
The strategy pair is obviously a signalling
convention.
 It solves the coordination problem.
 It is arbitrary.

Meaning of the Signals
Given the signalling convention before:
 0 lanterns in the belfry means that the
British are staying home.
 1 lantern in the belfry means that the
British are setting out by land.
 2 lantern in the belfry means that the
British are setting out by sea.
Some Remarks about
the General
Perspective




Assumption: speaker and hearer use language
according to a given semantic convention.
Goal: Explain how implicatures can emerge out
of semantic language use.
Non-reductionist perspective with respect to
semantic meaning.
Reductionist perspective with respect to
implicated meaning
Implicated meaning is in general not part of
conventional meaning:
 A stands in front of his obviously
immobilised car.
A: I am out of petrol.
B: There is a garage around the corner.
+> The garage is open
PCIs and GCIs
The goal is a foundational one.
 All implicatures will be treated as
particularised conversational implicatures
(PCIs).
 We will not discuss generalised
conversational implicatures (GCIs) or
Grice’ conventional implicatures.

The Agenda
Putting Grice on Lewisean feet!

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